Answer:
For the first example, the constant of proportionality should be .4 of a mile, meaning that Li can run .4 mile per minute. The equation should be .4x = y. For the second example, it is easy to find the constant of proportionality because it is given, which is 2. The equation to represent this would be 2x = y.
Step-by-step explanation:
The reason why the constant of proportionality is .4 is because I used the ratio from before and compared it to the one needed. I simply turned the ratios into fractions and I cross multiplied before turning it into a equation to solve to find .4 as the constant of proportionality. The equation should be .4x = y because x = the amount of minutes Li ran, and y = the total amount of miles she ran. The reason why the constant of proportionality is 2 in the second problem is because Jennifer is paying 2 per pound, which is the unit rate. If we are looking at the cost per pound, it would mean that 2 is the constant of proportionality. The reason why the equation to represent this would be 2x = y is because x = the amount of pounds, and y = the total amount of money, which represents the situation.
Answer:
Since from the laws of exponents we have that x−n=1xn , it implies that we may write 18=8−1 . 18=123=2−3.
Step-by-step explanation:
Answer:
Step-by-step explanation:
7g = x miles
7 grade is x miles
8g = 7g + 15%
8 grad is 15% more than 7 grade
put what 7g is equal to into the 8g equation
8g = x + 15%
Answer:
![\displaystyle (-∞, 2\frac{1}{3}) ∪ (1, ∞) \\ \\ 2\frac{1}{3} > t \:OR\: 1 < t](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28-%E2%88%9E%2C%202%5Cfrac%7B1%7D%7B3%7D%29%20%E2%88%AA%20%281%2C%20%E2%88%9E%29%20%5C%5C%20%5C%5C%202%5Cfrac%7B1%7D%7B3%7D%20%3E%20t%20%5C%3AOR%5C%3A%201%20%3C%20t)
Step-by-step explanation:
3t + 2 < 7 OR −4t + 5 < 1
- 2 - 2 - 5 - 5
___________________
![\displaystyle \frac{3t}{3} < \frac{7}{3} \:OR\: \frac{-4t}{-4} < \frac{-4}{-4} \\ \\ t < 2\frac{1}{3} \:OR\: t >1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B3t%7D%7B3%7D%20%3C%20%5Cfrac%7B7%7D%7B3%7D%20%5C%3AOR%5C%3A%20%5Cfrac%7B-4t%7D%7B-4%7D%20%3C%20%5Cfrac%7B-4%7D%7B-4%7D%20%5C%5C%20%5C%5C%20t%20%3C%202%5Cfrac%7B1%7D%7B3%7D%20%5C%3AOR%5C%3A%20t%20%3E1)
**Whenever you divide\multiply by a <em>negative</em><em> </em><em>integer</em>, you reverse the inequality symbol given to you <em>initially</em>.
<u>Extended</u><u> </u><u>Information</u><u> </u><u>on</u><u> </u><u>Inequalities</u>
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Answer:
Probability to draw a club and second card is red without replacement will be
or 12.75%
Step-by-step explanation:
A standard deck of cards contains number of cards = 52
And a standard deck contains number of club = 13
Now the probability of first card to be a club will be
![P_{1}=\frac{\text{Number of club in a deck}}{\text{Total number of cards}}](https://tex.z-dn.net/?f=P_%7B1%7D%3D%5Cfrac%7B%5Ctext%7BNumber%20of%20club%20in%20a%20deck%7D%7D%7B%5Ctext%7BTotal%20number%20of%20cards%7D%7D)
= ![\frac{13}{52}=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B52%7D%3D%5Cfrac%7B1%7D%7B4%7D)
Now this card is separated from the deck.
Therefore, number of remaining cards = 52 - 1 = 51
Second card has been drawn from the deck without replacement.
Since number of red cards in the deck = 13 + 13 = 26
Probability of the second card drawn = ![\frac{\text{Number of red cards}}{\text{Number of remaining cards}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BNumber%20of%20red%20cards%7D%7D%7B%5Ctext%7BNumber%20of%20remaining%20cards%7D%7D)
![P_{2}=\frac{26}{51}](https://tex.z-dn.net/?f=P_%7B2%7D%3D%5Cfrac%7B26%7D%7B51%7D)
Now probability that the first card is a club and the second card is red = ![P_{1}\times P_{2}=\frac{1}{4}\times \frac{26}{51}](https://tex.z-dn.net/?f=P_%7B1%7D%5Ctimes%20P_%7B2%7D%3D%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cfrac%7B26%7D%7B51%7D)
= ![\frac{13}{102}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B102%7D)
Or
%
Therefore, probability to draw a club and second card is red without replacement will be
or 12.75%